The Hornets fell to a 2-1 home defeat at Leeds on Saturday which paved the way for Hull to pip them to the final automatic spot.
Zola admitted that results had delivered a hammer blow to his players' morale but that they will be ready for their play-off semi-final first leg against Leicester on Thursday.
He told the Independent: "I know how tough this is for all of my players. Everyone is gutted.
"It's not a nice feeling to know you came so close and then right at the end to see things go wrong, but that is football.
"You just have to stay positive. It is deflating, but we have a good bunch here."
The Italian continued: "Not a lot of people get two chances at promotion, two bites at the cherry, but we have that. Now we have to go back and see if we can do it that way."
"I can assure you we are not going to approach the play-offs feeling sorry for ourselves, otherwise we will concede too much advantage to our rivals. We will do everything possible to make sure they are up for it."